Interaction of Finitely-Strained Viscoelastic Multipolar Solids and Fluids by an Eulerian Approach

Abstract

A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin–Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The no-slip contact between fluid and solid is considered and the Eulerian-frame return-mapping technique is used for both the fluid and the solid models, which allows for a “monolithic” formulation of this fluid–structure interaction problem. Existence and a certain regularity of weak solutions is proved by a Schauder fixed-point argument combined with a suitable regularization.